where wi is the net wage on segment i, yi is virtual income for segment i, z represents socioeconomic variables, and α, β, and γ are the parameters
to be estimated. For fixed α, β, and -γ, desired hours,

may be greater or less than the hours at the end points of
the budget segment Hi-1 and Hi. If desired hours are feasible, the indifference curve and the budget segment are tangent. If the budget set is convex,
this tangency is unique, and I then use the stochastic specification for the
deviation of actual hours from desired hours for person j as

Because observed hours hj ≥ 0, the stochastic term ηj is assumed to be
independent truncated normal across individuals in the population. This
assumption yields a Tobit specification for the hours-worked variable.
However, if

= 0, I assume that the individuals choose not to work
and set hj = 0. Because the final model has two sources of stochastic
variation, the interpretation of ηj differs from that of the error term in
standard models. Here the individual chooses, among jobs that differ in
normal (long-run) hours worked, the one with working hours closest to
his

. But observed hj may differ because of unexpected layoffs, short
time, overtime, or the worker's poor health together with measurement
error. As an empirical matter, the standard deviation of ηj is reasonably
small, indicating that people successfully match jobs to their desired
hours of work.

is chosen that leads to maximum utility, which is determined by the use of the corresponding indirect utility
function from equation 4. Again I use the stochastic specification of equation 6 to express the deviation of actual hours from desired hours of
work. It is interesting to note that, although certain kink points such as
H + ̃ in figure 5 in the nonconvex case cannot correspond to desired hours,

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